This project seeks to estimate sport fish harvest and releases of rockfish in Alaska waters by improving on the Howard et al. (2020) methods and expand the time series back to 1977 when the statewide harvest survey (SWHS) was first implemented. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and replaces the Howard decision tree approach to low sample sizes with a hierarchical model. The methods and results for generating harvest estimates are generally consistent between the Bayesian model and the Howard methods. Harvest estimates are consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data.

The Bayesian methods depart from the Howard method in how releases are estimated. The Howard methods assume that the species composition of the harvests are equal to the species composition of released fish, which is clearly contraindicated in the logbook data. For instance, logbook data demonstrates that yelloweye have been retained at high levels up until restrictions were enacted in recent years, whereas pelagic rockfish were released in significant numbers in the past with retention increasing in recent years as they have become more prized by anglers. Recent prohibition on retaining yelloweye in Southeast Alaska highlights the shortcomings of the original Howard assumptions as the species composition of the harvest would indicate that no yelloweye were caught and released during the closure.

The Howard method for estimating releases for private anglers also relied on an expansion of the logbook release estimates based on the ratio of private:guided releases of all rockfish in the SWHS. In addition to the faulty assumptions about species composition, this method ignores potential bias in SWHS estimates of harvests and releases or at least assumes that the bias in release and harvests are the same. As demonstrated in Figure 1, the bias in those two quantities appears to be quite different based on the logbook data. The Bayesian model thus attempts to estimate release probabilities based on the logbook data coupled with bias corrected estimates from the SWHS.

Lastly, the Howard methods were only used on data beginning in 1999 with the advent of the logbook program and estimates of harvests and releases prior to that have been based on linear ramps from 1999 back to the perceived start of the fishery. The Bayesian methods allow us to expand the time series back to 1977 when the SWHS was implemented by leveraging regional data trends in species composition and the proportion of caught rockfish harvested by species and/or species complex. Key advantages of the Bayesian approach are highlighted in table 1.

Table 1. Summary of key improvements in reconstructiing sport fish removals of rockfish using the Bayesian model as compared to the Howard et al. (2020) methods.
Issue Howard Bayes
Time series 1999 - present 1977 - present
Bias in SWHS Not explicitly dealt with. Relies on logbook data and ratios of guided/unguided from SWHS data to estimate unguided releases and harvests. Explicitly estimates bias in SWHS harvest and release estimates based on logbook data.
Species composition of releases Assumes that species composition of releases is equal to that of the harvest, which is not evident in the logbook data. Recognizes different release probabilities by species / species assemblage and estimates it from logbook data and bias corrected SWHS data
Sample size limitations Uses sample size threshholds such that when areas fall below those threshholds values are borrowed from nearby areas. Uses a hierarchichacal modelling approach that shares information between areas in the same region. Thus all data is used, even with small sample sizes. This is a more sound method that avoids assumptions and uses all of the data.
Error propogation Error is propogated when variance estimates are available, but there is uncertainty associated with borrowing values from nearby areas, or the assumption of species compositions being identical in harvest and releases, are not dealt with. By breaking the assumption that species composition is equal between harvests and releases, uncertainty in the release estimates is more reflective of the fishery. Furthermore, the hyerarchichal approach more accurately captures uncertainy within and between areas within a region.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are overall harvest estimates from 1977- 1995 and release estimates from 1990-1995 that required some partitioning to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied to the pre-1996 values.

**Figure 1.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units. Note that initial rockfish harvest estimates were not differentiated into species assemblage or species until 1998 when logbooks began differentiating by pelagic and non-pelagic. Logbooks began to collect data on yelloweye beginning in 2006. Port sampling programs to gather data on species composition of harvests began in 1996 in Southcentral and Kodiak and in 2006 in Southeast.

Figure 1.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units. Note that initial rockfish harvest estimates were not differentiated into species assemblage or species until 1998 when logbooks began differentiating by pelagic and non-pelagic. Logbooks began to collect data on yelloweye beginning in 2006. Port sampling programs to gather data on species composition of harvests began in 1996 in Southcentral and Kodiak and in 2006 in Southeast.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook records are a census of guided harvests and releases.

SWHS Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides have been required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 2.**- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).

Figure 2.- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).


A note on model development

To evaluate the discrepancy in apparent bias in harvest and release data, several models were explored to estimate releases during model development. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treated the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases. This tensions eventually highlighted the different release/retention probabilities between yelloweye and pelagics in the logbook data and prompted the current approach whereby that probability was calculated for the three main species complexes covered in the data: pelagics, yelloweye, and “other”. The methods described here follow the (\(LB_{fit}\)) formulation. Based on model behavior it is unlikely that the (\(LB_{cens}\)) model would work as there would not be enough data to estimate release probabilities. However, it may be worth running the (\(LB_{hyb}\)) approach as a sensitivity test at the very least.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish. In Southeast Alaska, the number of Demersal Shelf Rockfish (DSR, of which yelloweye are one species) and slope rockfish are also recorded.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta0_{(comp)ayu} + \frac{\beta1_{(comp)ayu}}{(1 + exp(\beta2_{(comp)ayu}*(y - \beta3_{(comp)ayu})))} + \beta4_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior. \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernible change in composition over the observed time period. \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was used for hindcasting.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested, \(pH_{(comp)ayu}\), by area, year, user group and species grouping. Because release data from the SWHS is for all rockfish and the release data from logbooks is only subdivided into pelagics, yelloweye and “other” (non-pelagic, non-yelloweye), we only estimated \(pH_{(comp)ayu}\) for those categories. Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases. For non-yelloweye DSR and Slope rockfish assemblages in Southeast Alaska \(R_{(DSR)ayu}\) and \(R_{(slope)ayu}\) were estimated from \(R_{(other)ayu}\) using the species composition data from the harvest, thus assuming that slope and DSR assemblages were caught and released at the same rates.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta0_{(pH)ayu} + \frac{\beta1_{(pH)ayuc}}{(1 + exp(\beta2_{(pH)ayuc}*(y - \beta3_{(pH)ayuc})))} + \beta4_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990. As with the compositional trends, \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernable change in harvest probability over the observed time period, \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was applied.

Release mortality (i.e., the number of released rockfish expected to die) was calculated assuming fixed mortality rates developed in each of the regions. Deep water release (DWR) devices were mandated for charter fleets in 2013 and rates were derived from CITATION. Southeast applies basic rates estimated in these studies while Southcentral and Kodiak rates were derived by using historical depth-of-release data to adjust the rates based on area and user group.

The total number of mortalities by year, area, user and species/species assemblage in numbers was calculated by summing harvests and release mortality such that

\[\begin{equation} M_{(comp)ayu}~=~ H_{(comp)ayu} + m_{R-(comp)ayu} * R_{(comp)ayu} \end{equation}\]

where \(m_{R-(comp)ayu}\) is the release mortality rate by year, area, user and species (Figure XX).

Total removals in biomass were converted using the average weight of fish from port sampling?. A minimum sample size per year of X fish was used as the cutoff for including in the data set. Weights were modeled hierarchically to estimate weights in years when data was missing. The total biomass of removals by year, area, user and species was thus

\[\begin{equation} B_{(comp)ayu}~=~ \overline{wt}_{(comp)ayu} * M_{(comp)ayu} \end{equation}\]

where \(\overline{wt}_{(comp)ayu}\) is the mean weight by species, area, user and year.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. As such, the release data are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), a second approaches was considered that loosened the assumption that logbook releases were a census. Methods explored to develope \(LB_{hyb}\) and \(LB_{cens}\) models are detailed at the end of this section.

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs was thus a proportion of the pelagic harvests

\[\begin{equation} x_{(black)ayu}~\sim~\textrm{Binomial}(P_{(black)ayu}, N_{ayu}^{pel}) \end{equation}\]

Yelloweye rockfish in Southcentral and Kodiak were modeled similarly as a proportion of the total number of non-pelagics such that

\[\begin{equation} x_{(yellow_{R2})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R2})ayu}, N_{ayu}^{nonpel}) \end{equation}\]

Southeast areas have several other non-pelagic groupings such that DSR and slope rockfish are a proportion of non-pelagics

\[\begin{equation} x_{(DSR)ayu}~\sim~\textrm{Binomial}(P_{(DSR)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

and

\[\begin{equation} x_{(slope)ayu}~\sim~\textrm{Binomial}(P_{(slope)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

with yelloweye in southeast a proportion of the DSR harvest

\[\begin{equation} x_{(yellow_{R1})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R1})ayu}, N_{ayu}^{DSR}). \end{equation}\].

Kodiak has limited port sampling beyond the main harbors but has a robust hydroacoustic survey that is used to quantify black rockfish abundance across the management area and uses stereocameras to derive species compositions of the hydroacoustic data. This data was used as supplementary data to further inform the model to the proportion of pelagic rockfish that are black in Kodiak areas. Angler landings in Kodiak show a higher proportion of black rockfish relative to the hydroacoustic survey and thus the proportion of black rockfish in the hydroacoustic sample related to the true proportion such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ P_{(black|pelagic)ayu} + ae_{au} \end{equation}\].

where \(ae_{au}\) is the angler effect for each area and user group modeled hierarchically around a mean of 0. Predicted \(P_{(black|pelagic)ayu}^{HA}\) assumed a beta distribution such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ beta(\alpha_{HA},\beta_{HA}) \end{equation}\]

where

\[\begin{equation} \alpha_{HA} ~=~ (P_{(black|pelagic)ayu}^{HA})^2 * \frac{1 - P_{(black|pelagic)ayu}^{HA}}{\frac{var_{P_{HA}}-1}{P_{(black|pelagic)ayu}^{HA}}}, \end{equation}\]

\[\begin{equation} \beta_{HA} ~=~ (\alpha_{HA}) * \frac{1}{P_{(black|pelagic)ayu}^{HA} - 1}, \end{equation}\]

\[\begin{equation} var_{P_{HA}} ~=~ (P_{(black|pelagic)ayu}^{HA} * cvP_{(black|pelagic)ayu}^{HA})^2 \end{equation}\]

where \(cvP_{(black|pelagic)ayu}^{HA}\) is the coefficient of variation for the hydroacoustic proportions

\[\begin{equation} cvP_{(black|pelagic)ayu}^{HA} ~=~ \frac{\sqrt{varP_{(black|pelagic)ayu}^{HA}}}{P_{(black|pelagic)ayu}^{HA}} \end{equation}\]

and the variance is approximated using the XXXX method as

\[\begin{equation} varP_{(black|pelagic)ayu}^{HA} ~=~ (\frac{1}{n_{pel}})^2 * varN_{black} + (\frac{n_{black}}{n_{pel}^2}) * varN_{pel} \end{equation}\]

where \(varN_{black}\) and \(varN_{black}\) are the variance of the estimated number of black and pelagic rockfish in the hydroacoustic survey, respectively (CITATION).

The average weight of rockfish by species, user, area and year was modeled hierarchically at several levels within regions such that

\[\begin{equation} wt_{(comp)ayu} ~\sim~ Normal(wt_{(comp)au},\sigma_{wt_{(comp)au}}) ~\sim~ Normal(wt_{(comp)a},\sigma_{wt_{(comp)a}}) ~\sim~ Normal(wt_{(comp)region},\sigma_{wt_{(comp)region}}) \end{equation}\]

where region refers to Kodiak, Southcentral and Southeast. Mean weights and variance were calculated as XXX.

Alternative likelihoods for release estimates

To loosen the assumption that logbook release data are an effective census of true releases I explored models that treated logbook release estimates as a lower bound on the estimate of true releases. In a hybrid approach yelloweye and non-pelagic releases are regarded as a reliable census (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates (where censoring implies NA values) such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

This model formulation failed such that there was not enough data to inform pelagic releases and the values did not seem valid. A second approach is being explored that fits the censored data using a lognormal distribution centered around the logbook release value, but also with a lower bound equal to the number of recorded releases such that

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Logbook data is assumed to be a census and as such there is no estimate of uncertainty. As of this writing, several methods are being examined for how to treat \(\sigma_{Ray1}^2\). Models are being run that attempt to allow the model to estimate \(\sigma_{Ray1}^2\) with priors. A simple model applies a uniform prior (0.1,50) to \(\sigma_{Ray1}^2\). A hierarchichal approach based on regions is also being examined whereby \(\sigma_{Ray1}^2\) is lognormally distributed around hyper priors \(\mu_{\sigma_R}\) and \(\sigma_{\sigma_R}\). Initial efforts have applied a uniform prior on \(\mu_{\sigma_R}\) between 1 and 50 and on \(\sigma_{\sigma_R}\) between 0 and 10.

Priors.

Priors range from uninformative to very informative or fixed. Priors for compositional logistic parameters are in Table 2 and proportion harvest logistic parameters are in Table 3. Until I figure out how to make a nice table in Rmarkdown, please refer to the attached spreadsheet and comp and harvp tabs.

Unresolved issues and outstanding questions:

  1. Reliability of unguided release estimates: These estimates have the least information feeding them and rely on the bias-corrected SWHS release estimates of all rockfish and the trends in release probability evident in the logbook data. The \(\beta4\) term that estimates the guided/unguided effect was given a very informative prior that tied the release probability of private anglers tightly to that of the charter fleet. The model is then trying to balance the three species complex estimates (pelagic, yelloweye and other) so that they sum to the total unguided releases estimated from the bias corrected SWHS data. For the most part this seems reasonable and appears to work, but there are certain areas where the estimates are “wonky”:

    1. Total rockfish releases more or less align with the total releases estimated with the Howard methods. Presumably, much of the discrepancy results from the substantial bias in release estimates from the SWHS. Interestingly, the logbook data indicates that the SWHS underestimates harvests but overestimates releases by a significant factor (Figure 23 and 24 below).
    2. In general, release estimates of black rockfish are substantially lower than those calculated using the Howard methods. Presumably, much of this derives from the bias correction of the SWHS release estimates.
    3. Yelloweye release estimates also differ considerably from the Howard estimates, but unlike black rockfish are sometimes lower and sometimes higher. Two areas in particular are a little head scratching. Yelloweye releases in the Kodiak Northeast area in particular are significantly lower than for guided anglers with the same pattern evident in Cook Inlet to a lesser extent. Cook Inlet yelloweye numbers are very small, so this is a sample size issue with little consequence. The cause of the Kodiak northeast estimates is not clear to me at this point, but the model estimates the proportion harvested by unguided anglers to be much lower than that of guided anglers, even with the informative prior on \(\beta4\). This must be a product of the bias corrected SWHS release estimates and how the model is partitioning that estimate into the 3 species complexes, but itis a bit a of head scratcher.
  2. Proportion guided estimates: There is not much data on this proportion prior to 2011 and it is not modeled with any sort of trend as was done for species composition and harvest proportions. With the exception of Cook Inlet and North Gulf Coast areas, there is little, if any, trend apparent in the data and perhaps this approach is the best available given the data available. However, if there are data sources somewhere that could inform this part of the model they could be incorporated.

  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.

  4. Proportion harvest estimates for non-pelagic, non-yelloweye in Kodiak WKMA: I need to adjust the prior on the inflection point, \(\beta3\), so that it is forced to occur after 2006. Right now the model is estimating inflection in two Kodiak areas before that point where there is no data to justify a shift. The current inflection is a result of the hierachichal model.

  5. Proportion pelagic in PWS and CSEO: The parameters for these particular proportions are very slow to converge. For the CSEO, the estimates of the \(\beta\) parameters are similar to the other Southeast areas, but the mixing is poor over the length of the chains. In this case I think they will ultimately converge with a very long model run and the shape of the curve in the model output looks acceptable. For the two PWS areas the model seems to struggle with the disparate proportional data from the logbook and the port sampling. There is some wandering in the chains of the \(\beta0\) and \(\beta1\) terms and spikiness in the \(\beta2\) terms. I’ve been working on constraining the hyperpriors for PWS \(beta2\). Similar to CSEO, it may just entail a very long model run to reach convergence, but the shape of the curves looks reasonable.

Next steps:

Once the model is finalized, harvest and release numbers need to be converted into biomass removals. This is a two step process where release mortality estimates are applied to the release estimates to estimate the number of released rockfish that do not survive. This is based on studies and will reflect the values that the department has been using with the Howard methods. Region 2 (both Southcentral and Kodiak) have release-at-depth estimates from a number of years that they apply across all years and then calculate mortality rates based on those estiates. Southease does not have release-at-depth data and simply applies an assumed rate based on research.

Once release mortality is calculated average weight data is applied to convert numbers to biomass. The plan is to incorporate all of this into the model to propogate uncertainty into the posteriors. However, the model already takes a long time to run and I may explore a simpler approach using the posteriors from the numbers model to speed up processing.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 3.**- Total rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.





**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.





**Figure 8.**- DSR rockfish (excluding yelloweye) harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 8.- DSR rockfish (excluding yelloweye) harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 9.**- DSR rockfish releases (including yelloweye) 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 9.- DSR rockfish releases (including yelloweye) 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 11.**- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 11.- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 12.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 12.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Total Biomass Removal Estimates

**Figure 13.**- Black rockfish estimated total removals in lbs in 1996--2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 13.- Black rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.



**Figure 14.**- Yellow rockfish estimated total removals in lbs in 1996--2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 14.- Yellow rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

**Figure 15.**- Pelagic rockfish estimated total removals in lbs in 1996--2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 15.- Pelagic rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.


**Figure 16.**- Non-yelloweye, demersal shelf rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 16.- Non-yelloweye, demersal shelf rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.


**Figure 17.**- Slope rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 17.- Slope rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.


Model fit

Logbook residuals

**Figure 18.**- Residuals from logbook harvests.

Figure 18.- Residuals from logbook harvests.


SWHS residuals

**Figure 19.**- Residuals from SWHS harvests.

Figure 19.- Residuals from SWHS harvests.



**Figure 20.**- Residual of SWHS releases.

Figure 20.- Residual of SWHS releases.

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 21.**- Mean percent of harvest by charter anglers.

Figure 21.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although the model smooths out the changes and we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 22.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 22.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 23.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 23.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 24.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 24.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 25.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 25.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.


## NULL


## NULL

SWHS bias

Figure 23 shows the mean estimate for SWHS bias in harvests and releases. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias. Bias in release estimates is substantial and whereas the SWHS appears to underestimate harvests, it appears to greatly overestimates releases by a factor of 2 or more in most areas as derived from logbook reported releases.

**Figure 28.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 28.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS harvest bias track observations fairly well when he have guided harvest estimates. The estimates of release bias in the SWHS data track observed patterns to an extent, but appear to smooth these more volatile disagreements with the logbook data. Adam postulated in his initial start on this that some of this could be the result of the estimates of the proportion guided. This value was not modelled with a trend and thus applies a constant estimate when hindcasting. Data on these relationships could greatly improve this model.

**Figure 29.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 29.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 25 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 30.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 30.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment. For the most part, P(black|pelagic) is relatively constant across areas, with the exception of Cook Inlet and NSEI in Southeast AK. It may be worth discussing whether the shifts in those areas is a result of improved or changing species identification rather than actual shift in the species composition of the catch.

**Figure 31.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023. Kodiak panels include data from a hydroacoustic survey and the proportion of pelagic rockfish that are black in those areas (red) and the adjusted proportions based on obseved harvests for charter (blue) and private (cyan) users.

Figure 31.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023. Kodiak panels include data from a hydroacoustic survey and the proportion of pelagic rockfish that are black in those areas (red) and the adjusted proportions based on obseved harvests for charter (blue) and private (cyan) users.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 32.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 32.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 33.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 33.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 34.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 34.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



P(slope|non-pelagic & non-yellowye) For release estimates

**Figure 35.**- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.

Figure 35.- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.



Weight Fits

**Figure 36.**- Mean weights of black rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 36.- Mean weights of black rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 37.**- Mean weights of yelloweye rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 37.- Mean weights of yelloweye rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 38.**- Mean weights of non-black, pelagic rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 38.- Mean weights of non-black, pelagic rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 39.**- Mean weights of non-yelloweye, demersal shelf rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 39.- Mean weights of non-yelloweye, demersal shelf rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 40.**- Mean weights of slope rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 40.- Mean weights of slope rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


### Summary of unconverged parameters:

Table X. Unconverged parameters.

## [1]  3  1  0  2 NA
##          variable index     Rhat index_n
## 1 tau_beta2_slope  <NA> 1.203364      NA

area

variable

year

user

species

Rhat

BSAI

Ro_ayu

7

1.289515

BSAI

Ro_ay

7

1.289422

BSAI

Ro_ayu

8

1.278959

BSAI

Ro_ay

8

1.278292

BSAI

Ry_ay

7

1.247618

BSAI

Ry_ayu

7

1.247553

BSAI

Ro_ayu

44

1.240458

BSAI

Ro_ay

44

1.239136

BSAI

Ro_ayu

29

1.238620

BSAI

Ro_ay

29

1.238150

BSAI

Ro_ayu

3

1.227576

BSAI

Ro_ay

3

1.223786

BSAI

Ro_ayu

12

1.215138

BSAI

Ry_ayg

15

1.212564

BSAI

Ro_ay

12

1.211061

BSAI

Ro_ayu

43

1.204786

BSAI

Ro_ay

43

1.202564

BSAI

Rb_ayu

10

1.201175

BSAI

Ro_ayu

11

1.199253

BSAI

Rp_ayu

10

1.198552

BSAI

R_ayu

10

1.198352

BSAI

Ro_ay

11

1.196522

BSAI

Rb_ay

10

1.196021

BSAI

Rp_ay

10

1.193324

BSAI

R_ay

10

1.193031

BSAI

Ro_ayu

13

1.189761

BSAI

Ry_ayu

18

1.187908

BSAI

Ry_ayg

8

1.183686

BSAI

Ro_ayg

4

1.182951

BSAI

Ry_ayg

18

1.181138

BSAI

Ry_ay

18

1.176250

BSAI

H_ayu

10

1.171104

BSAI

Ro_ayu

40

1.170907

BSAI

Ry_ayg

11

1.170101

BSAI

Hb_ayu

10

1.169720

BSAI

Ro_ay

4

1.169142

BSAI

Ro_ayg

13

1.168547

BSAI

Ry_ay

20

1.168005

BSAI

Hp_ayu

10

1.167915

BSAI

Ry_ayu

20

1.165533

BSAI

Ro_ay

40

1.163968

BSAI

Ro_ayu

9

1.163792

BSAI

Ro_ay

9

1.156401

BSAI

Ry_ayu

28

1.153717

BSAI

Hb_ay

10

1.153437

BSAI

Hy_ayg

3

1.153026

BSAI

Ro_ayu

4

1.152817

BSAI

Hp_ay

10

1.151909

BSAI

H_ay

10

1.151476

BSAI

Ro_ayg

16

1.150310

BSAI

Ry_ay

28

1.149596

BSAI

Ro_ay

13

1.149258

BSAI

Ro_ayu

10

1.142740

BSAI

Ry_ay

4

1.142707

BSAI

Ro_ayu

41

1.140923

BSAI

Ro_ayu

2

1.139452

BSAI

Ro_ay

41

1.138435

BSAI

Ro_ayg

1

1.136301

BSAI

Ro_ay

2

1.133424

BSAI

Ry_ayg

9

1.133415

BSAI

Hy_ayu

10

1.133148

BSAI

Ro_ay

10

1.130224

BSAI

Ry_ayg

21

1.129706

BSAI

Ro_ayu

36

1.127807

BSAI

Ro_ay

36

1.126235

BSAI

Ro_ayu

17

1.126198

BSAI

Ry_ayu

4

1.123696

BSAI

Ro_ayu

37

1.123308

BSAI

Hy_ay

10

1.122866

BSAI

Ro_ayu

25

1.122420

BSAI

Rp_ayg

14

1.121566

BSAI

Ro_ayu

14

1.120851

BSAI

Ro_ay

37

1.120217

BSAI

Ro_ay

25

1.119317

BSAI

R_ayg

14

1.118741

BSAI

Ro_ay

17

1.116339

BSAI

Ry_ayu

9

1.115860

BSAI

Ro_ayg

20

1.114785

BSAI

Ro_ayg

7

1.114566

BSAI

Ho_ayu

11

1.111867

CI

Ro_ayu

6

1.154241

CI

tau_beta1_black

1.147891

CI

Ro_ay

6

1.128774

CI

R_ayu

6

1.116724

CSEO

pH

47

2

2

1.151249

CSEO

pH

46

2

2

1.121781

CSEO

pH

45

2

2

1.116405

EWYKT

beta1_dsr

1.170934

EWYKT

p_dsr

29

1

1.169228

EWYKT

p_dsr

15

2

1.153081

EWYKT

p_dsr

3

2

1.143496

EWYKT

p_dsr

29

2

1.140725

EWYKT

p_dsr

6

1

1.134414

EWYKT

Rs_ayu

18

1.132715

NG

Ro_ayu

12

1.148070

NG

mu_beta2_pH

1

1.135154

NG

Ro_ay

12

1.132014

NSEI

beta2_pelagic

1.164295

NSEO

Ry_ayg

8

1.130843

NSEO

Rs_ayu

20

1.115677

NSEO

Rdnye_ayu

44

1.112313

PWSI

beta1_pelagic

1.138339

PWSI

beta1_pH

2

1.127972

PWSI

beta2_pelagic

1.124632

PWSI

beta0_pelagic

1.118883

PWSO

beta1_pH

2

1.255959

PWSO

beta0_pelagic

1.154732

PWSO

Ro_ayg

10

1.124090

SOKO2SAP

Ro_ayu

8

1.240603

SOKO2SAP

Ro_ay

8

1.235025

SOKO2SAP

Ro_ayu

6

1.222857

SOKO2SAP

Ro_ayu

4

1.217302

SOKO2SAP

Ro_ay

6

1.209331

SOKO2SAP

Ro_ay

4

1.200623

SOKO2SAP

Rp_ayu

1

1.190479

SOKO2SAP

R_ayu

1

1.190217

SOKO2SAP

Rb_ayu

1

1.187755

SOKO2SAP

Rp_ay

1

1.187621

SOKO2SAP

R_ay

1

1.187278

SOKO2SAP

Rb_ay

1

1.185125

SOKO2SAP

beta1_pH

3

1.183784

SOKO2SAP

Ro_ayu

7

1.159351

SOKO2SAP

beta4_pelagic

1.144051

SOKO2SAP

Ry_ayu

17

1.141310

SOKO2SAP

Ro_ay

7

1.140390

SOKO2SAP

Ry_ay

17

1.137240

SOKO2SAP

Ro_ayu

2

1.132917

SOKO2SAP

Ro_ayu

30

1.132727

SOKO2SAP

Ro_ay

30

1.131246

SOKO2SAP

Ro_ay

2

1.130836

SOKO2SAP

Rb_ayu

6

1.128360

SOKO2SAP

Rb_ay

6

1.125331

SOKO2SAP

Rp_ayu

6

1.125100

SOKO2SAP

Ro_ayg

3

1.124743

SOKO2SAP

R_ayu

6

1.124736

SOKO2SAP

Rp_ay

6

1.122022

SOKO2SAP

R_ay

6

1.121545

SOKO2SAP

Rp_ayu

4

1.121435

SOKO2SAP

R_ayu

4

1.121043

SOKO2SAP

Rb_ay

3

1.120989

SOKO2SAP

Rb_ayu

3

1.120135

SOKO2SAP

Rp_ay

4

1.120013

SOKO2SAP

R_ay

4

1.119568

SOKO2SAP

Ry_ayu

18

1.118856

SOKO2SAP

Rp_ayu

3

1.118499

SOKO2SAP

R_ayu

3

1.118356

SOKO2SAP

Rp_ay

3

1.118148

SOKO2SAP

R_ay

3

1.117876

SOKO2SAP

Ry_ay

18

1.117494

SOKO2SAP

Rb_ayu

4

1.115677

SOKO2SAP

Rb_ay

4

1.114430

SOKO2SAP

Ro_ayu

16

1.114077

SSEI

lambda_H

1.274730

SSEI

pH

45

2

2

1.154535

SSEI

pH

47

2

2

1.128255

SSEO

Rp_ayu

3

1.128743

SSEO

Rb_ayu

1

1.127580

SSEO

Rb_ayu

3

1.126252

SSEO

Rp_ayu

2

1.126014

SSEO

Rb_ayu

2

1.124639

SSEO

R_ayu

3

1.121612

SSEO

Rp_ayu

1

1.117196

WKMA

beta2_pH

1

1.274047

WKMA

Ro_ayu

9

1.141892

WKMA

Ro_ay

9

1.126323

WKMA

beta1_pH

1

1.116633

WKMA

beta0_pH

1

1.114032

afognak

Ro_ayu

16

1.198001

afognak

Ro_ay

16

1.173554

afognak

Ry_ayu

12

1.169819

afognak

Ry_ay

12

1.167018

afognak

Hy_ayu

12

1.146442

afognak

Ho_ayu

18

1.125921

eastside

Ry_ayg

25

1.194423

eastside

Hy_ayu

20

1.159150

eastside

Ry_ayu

8

1.158094

eastside

Ry_ay

8

1.153888

eastside

Ro_ayu

12

1.149363

eastside

Ro_ayu

7

1.135179

eastside

Hy_ayu

35

1.125312

eastside

Ro_ayu

2

1.123124

eastside

Ro_ayu

24

1.116545

eastside

Ro_ayg

8

1.113801

eastside

Ro_ayu

21

1.110660

northeast

Ry_ayu

9

1.120526

northeast

Ry_ay

9

1.119536

tau_beta2_slope

1.203364

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.125 0.075 -0.261 -0.128 0.036
mu_bc_H[2] -0.096 0.044 -0.171 -0.099 -0.001
mu_bc_H[3] -0.434 0.070 -0.565 -0.437 -0.289
mu_bc_H[4] -0.991 0.193 -1.377 -0.990 -0.617
mu_bc_H[5] 0.902 0.920 -0.184 0.721 3.214
mu_bc_H[6] -2.158 0.313 -2.752 -2.155 -1.556
mu_bc_H[7] -0.458 0.109 -0.683 -0.453 -0.250
mu_bc_H[8] 0.248 0.354 -0.325 0.220 1.050
mu_bc_H[9] -0.291 0.133 -0.541 -0.294 -0.021
mu_bc_H[10] -0.099 0.071 -0.227 -0.102 0.047
mu_bc_H[11] -0.123 0.038 -0.196 -0.123 -0.049
mu_bc_H[12] -0.254 0.109 -0.492 -0.250 -0.051
mu_bc_H[13] -0.137 0.077 -0.288 -0.139 0.018
mu_bc_H[14] -0.306 0.096 -0.503 -0.301 -0.133
mu_bc_H[15] -0.342 0.049 -0.437 -0.342 -0.243
mu_bc_H[16] -0.262 0.371 -0.913 -0.291 0.566
mu_bc_R[1] 1.317 0.142 1.045 1.316 1.601
mu_bc_R[2] 1.454 0.095 1.269 1.454 1.643
mu_bc_R[3] 1.392 0.144 1.105 1.392 1.679
mu_bc_R[4] 0.916 0.197 0.506 0.923 1.276
mu_bc_R[5] 1.198 0.456 0.286 1.207 2.062
mu_bc_R[6] -1.587 0.407 -2.394 -1.579 -0.813
mu_bc_R[7] 0.444 0.212 0.009 0.450 0.845
mu_bc_R[8] 0.536 0.188 0.152 0.540 0.890
mu_bc_R[9] 0.326 0.203 -0.106 0.342 0.688
mu_bc_R[10] 1.309 0.167 0.969 1.315 1.615
mu_bc_R[11] 1.037 0.097 0.853 1.036 1.223
mu_bc_R[12] 0.820 0.203 0.417 0.823 1.205
mu_bc_R[13] 1.029 0.102 0.829 1.029 1.223
mu_bc_R[14] 0.895 0.143 0.602 0.894 1.168
mu_bc_R[15] 0.782 0.110 0.566 0.785 0.993
mu_bc_R[16] 1.093 0.127 0.833 1.095 1.333
tau_pH[1] 5.122 0.436 4.311 5.107 6.037
tau_pH[2] 1.971 0.223 1.566 1.961 2.433
tau_pH[3] 2.150 0.220 1.739 2.145 2.599
beta0_pH[1,1] 0.558 0.173 0.206 0.564 0.874
beta0_pH[2,1] 1.367 0.184 0.995 1.372 1.704
beta0_pH[3,1] 1.428 0.193 1.024 1.440 1.772
beta0_pH[4,1] 1.565 0.217 1.090 1.580 1.940
beta0_pH[5,1] -0.863 0.301 -1.530 -0.840 -0.354
beta0_pH[6,1] -0.758 0.560 -2.030 -0.655 -0.079
beta0_pH[7,1] -0.489 0.576 -1.980 -0.439 0.500
beta0_pH[8,1] -0.664 0.271 -1.265 -0.636 -0.203
beta0_pH[9,1] -0.643 0.283 -1.270 -0.621 -0.134
beta0_pH[10,1] 0.348 0.218 -0.128 0.365 0.729
beta0_pH[11,1] -0.068 0.168 -0.408 -0.061 0.253
beta0_pH[12,1] 0.483 0.187 0.119 0.488 0.845
beta0_pH[13,1] 0.006 0.143 -0.268 0.006 0.289
beta0_pH[14,1] -0.303 0.167 -0.645 -0.295 0.007
beta0_pH[15,1] -0.019 0.178 -0.375 -0.016 0.331
beta0_pH[16,1] -0.472 0.403 -1.405 -0.395 0.063
beta0_pH[1,2] 2.828 0.161 2.498 2.833 3.115
beta0_pH[2,2] 2.886 0.140 2.606 2.886 3.159
beta0_pH[3,2] 3.129 0.160 2.837 3.125 3.438
beta0_pH[4,2] 2.949 0.132 2.690 2.952 3.203
beta0_pH[5,2] 4.757 1.391 2.936 4.483 8.535
beta0_pH[6,2] 3.119 0.209 2.715 3.121 3.526
beta0_pH[7,2] 1.831 0.200 1.433 1.829 2.222
beta0_pH[8,2] 2.871 0.175 2.537 2.866 3.228
beta0_pH[9,2] 3.438 0.220 3.019 3.432 3.875
beta0_pH[10,2] 3.686 0.212 3.260 3.682 4.108
beta0_pH[11,2] -4.848 0.296 -5.422 -4.852 -4.248
beta0_pH[12,2] -4.786 0.404 -5.596 -4.780 -4.005
beta0_pH[13,2] -4.563 0.405 -5.348 -4.582 -3.746
beta0_pH[14,2] -5.595 0.492 -6.624 -5.568 -4.729
beta0_pH[15,2] -4.289 0.343 -4.930 -4.291 -3.607
beta0_pH[16,2] -4.860 0.377 -5.622 -4.848 -4.118
beta0_pH[1,3] -0.108 0.702 -1.674 -0.026 1.009
beta0_pH[2,3] 2.195 0.159 1.885 2.194 2.514
beta0_pH[3,3] 2.528 0.147 2.243 2.528 2.820
beta0_pH[4,3] 2.967 0.161 2.650 2.967 3.279
beta0_pH[5,3] 2.151 1.314 0.502 1.883 5.463
beta0_pH[6,3] 0.995 0.493 -0.188 1.031 1.843
beta0_pH[7,3] 0.633 0.175 0.300 0.629 0.985
beta0_pH[8,3] 0.304 0.187 -0.063 0.309 0.661
beta0_pH[9,3] -0.644 0.393 -1.667 -0.606 0.001
beta0_pH[10,3] 0.475 0.378 -0.458 0.521 1.080
beta0_pH[11,3] -0.164 0.329 -0.809 -0.174 0.480
beta0_pH[12,3] -0.853 0.358 -1.640 -0.826 -0.236
beta0_pH[13,3] -0.112 0.311 -0.715 -0.116 0.492
beta0_pH[14,3] -0.280 0.263 -0.806 -0.277 0.235
beta0_pH[15,3] -0.714 0.310 -1.350 -0.695 -0.176
beta0_pH[16,3] -0.381 0.289 -0.957 -0.383 0.204
beta1_pH[1,1] 3.068 0.323 2.490 3.047 3.784
beta1_pH[2,1] 2.157 0.307 1.647 2.132 2.787
beta1_pH[3,1] 1.971 0.310 1.441 1.944 2.619
beta1_pH[4,1] 2.398 0.362 1.833 2.351 3.201
beta1_pH[5,1] 2.296 0.367 1.701 2.260 3.099
beta1_pH[6,1] 3.862 1.163 2.319 3.623 6.793
beta1_pH[7,1] 2.592 1.120 0.775 2.480 5.519
beta1_pH[8,1] 4.052 1.036 2.629 3.824 6.680
beta1_pH[9,1] 2.319 0.373 1.668 2.285 3.183
beta1_pH[10,1] 2.225 0.311 1.713 2.198 2.886
beta1_pH[11,1] 3.242 0.212 2.843 3.237 3.659
beta1_pH[12,1] 2.551 0.220 2.123 2.551 2.985
beta1_pH[13,1] 2.962 0.213 2.540 2.964 3.390
beta1_pH[14,1] 3.404 0.218 2.989 3.401 3.848
beta1_pH[15,1] 2.519 0.224 2.086 2.515 2.983
beta1_pH[16,1] 4.121 0.772 3.163 3.973 5.911
beta1_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,2] 0.006 0.080 0.000 0.000 0.001
beta1_pH[4,2] 0.000 0.003 0.000 0.000 0.001
beta1_pH[5,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[6,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[8,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[9,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[11,2] 6.687 0.332 6.021 6.687 7.322
beta1_pH[12,2] 6.446 0.464 5.588 6.423 7.392
beta1_pH[13,2] 6.939 0.442 6.069 6.947 7.826
beta1_pH[14,2] 7.239 0.518 6.317 7.212 8.341
beta1_pH[15,2] 6.757 0.377 6.010 6.753 7.495
beta1_pH[16,2] 7.454 0.414 6.643 7.447 8.288
beta1_pH[1,3] 4.647 1.623 2.118 4.409 8.159
beta1_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[5,3] 3.886 6.283 0.786 2.808 12.687
beta1_pH[6,3] 3.484 4.842 0.368 2.654 13.790
beta1_pH[7,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[8,3] 2.750 0.346 2.076 2.741 3.455
beta1_pH[9,3] 2.756 0.457 2.018 2.713 3.860
beta1_pH[10,3] 2.897 0.458 2.141 2.844 3.959
beta1_pH[11,3] 2.746 0.389 2.014 2.742 3.519
beta1_pH[12,3] 4.095 0.448 3.252 4.076 4.974
beta1_pH[13,3] 1.696 0.334 1.033 1.695 2.335
beta1_pH[14,3] 2.528 0.336 1.891 2.519 3.188
beta1_pH[15,3] 2.004 0.335 1.411 1.988 2.690
beta1_pH[16,3] 1.795 0.321 1.155 1.798 2.433
beta2_pH[1,1] 0.482 0.127 0.294 0.464 0.775
beta2_pH[2,1] 0.580 0.300 0.253 0.519 1.263
beta2_pH[3,1] 0.659 0.480 0.223 0.558 1.825
beta2_pH[4,1] 0.479 0.205 0.213 0.442 0.952
beta2_pH[5,1] 1.483 1.015 0.244 1.338 3.922
beta2_pH[6,1] 0.180 0.064 0.082 0.171 0.326
beta2_pH[7,1] 0.032 0.265 0.000 0.000 0.185
beta2_pH[8,1] 0.241 0.102 0.123 0.226 0.440
beta2_pH[9,1] 0.441 0.249 0.181 0.394 0.962
beta2_pH[10,1] 0.611 0.264 0.272 0.560 1.251
beta2_pH[11,1] 0.795 0.210 0.476 0.757 1.311
beta2_pH[12,1] 1.358 0.513 0.730 1.242 2.583
beta2_pH[13,1] 0.751 0.234 0.415 0.717 1.311
beta2_pH[14,1] 0.837 0.219 0.521 0.801 1.372
beta2_pH[15,1] 0.827 0.314 0.418 0.762 1.620
beta2_pH[16,1] 0.386 0.181 0.157 0.340 0.851
beta2_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,2] -1.999 1.819 -6.747 -1.511 -0.032
beta2_pH[4,2] -2.032 1.907 -6.896 -1.509 -0.025
beta2_pH[5,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[6,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[8,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[9,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[11,2] -9.554 4.370 -20.644 -8.546 -4.036
beta2_pH[12,2] -8.145 5.044 -20.388 -7.251 -1.020
beta2_pH[13,2] -7.941 4.997 -20.233 -6.909 -1.665
beta2_pH[14,2] -8.638 4.742 -20.589 -7.582 -2.539
beta2_pH[15,2] -9.382 4.418 -20.390 -8.323 -3.796
beta2_pH[16,2] -9.481 4.348 -20.488 -8.467 -3.910
beta2_pH[1,3] 0.241 0.270 0.101 0.182 0.690
beta2_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[5,3] 9.074 6.266 -0.073 8.256 23.518
beta2_pH[6,3] 9.080 6.347 0.182 8.028 23.900
beta2_pH[7,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[8,3] 10.032 5.797 1.776 8.864 24.171
beta2_pH[9,3] 9.040 6.398 0.499 7.868 23.833
beta2_pH[10,3] 8.508 6.529 0.507 7.469 23.657
beta2_pH[11,3] -2.374 2.151 -9.029 -1.730 -0.645
beta2_pH[12,3] -2.528 2.150 -9.099 -1.886 -0.926
beta2_pH[13,3] -2.949 2.386 -10.161 -2.162 -0.790
beta2_pH[14,3] -2.884 2.289 -9.277 -2.158 -0.928
beta2_pH[15,3] -3.063 2.426 -9.905 -2.254 -1.009
beta2_pH[16,3] -3.117 2.506 -10.314 -2.269 -0.961
beta3_pH[1,1] 35.957 0.825 34.387 35.966 37.633
beta3_pH[2,1] 33.532 1.203 31.442 33.409 36.076
beta3_pH[3,1] 33.657 1.050 31.619 33.640 35.848
beta3_pH[4,1] 33.862 1.252 31.626 33.770 36.623
beta3_pH[5,1] 27.675 1.093 26.407 27.451 30.979
beta3_pH[6,1] 38.168 3.210 32.272 37.982 44.784
beta3_pH[7,1] 30.642 8.035 18.600 30.058 45.168
beta3_pH[8,1] 40.062 2.191 36.295 39.776 45.060
beta3_pH[9,1] 30.663 1.477 28.106 30.562 33.965
beta3_pH[10,1] 32.963 0.984 31.107 32.947 34.950
beta3_pH[11,1] 30.340 0.473 29.451 30.332 31.307
beta3_pH[12,1] 30.153 0.402 29.354 30.152 30.941
beta3_pH[13,1] 33.152 0.582 32.010 33.132 34.352
beta3_pH[14,1] 32.039 0.463 31.163 32.022 32.978
beta3_pH[15,1] 31.207 0.649 29.902 31.215 32.477
beta3_pH[16,1] 32.092 1.100 30.407 31.925 34.744
beta3_pH[1,2] 30.029 8.001 18.477 29.109 45.058
beta3_pH[2,2] 30.026 7.930 18.610 29.079 44.765
beta3_pH[3,2] 30.134 8.044 18.554 28.940 44.961
beta3_pH[4,2] 30.058 7.939 18.544 29.298 44.827
beta3_pH[5,2] 29.759 7.839 18.441 28.692 44.638
beta3_pH[6,2] 30.062 7.949 18.489 29.094 45.013
beta3_pH[7,2] 29.898 7.852 18.520 28.899 44.917
beta3_pH[8,2] 29.796 7.959 18.381 28.723 45.033
beta3_pH[9,2] 30.154 7.921 18.559 29.403 44.939
beta3_pH[10,2] 29.978 7.887 18.481 28.913 44.944
beta3_pH[11,2] 43.399 0.180 43.110 43.383 43.769
beta3_pH[12,2] 43.193 0.194 42.943 43.147 43.727
beta3_pH[13,2] 43.864 0.152 43.469 43.907 44.044
beta3_pH[14,2] 43.305 0.205 43.047 43.251 43.801
beta3_pH[15,2] 43.408 0.197 43.100 43.388 43.812
beta3_pH[16,2] 43.496 0.186 43.165 43.495 43.836
beta3_pH[1,3] 39.227 3.239 33.070 39.095 45.371
beta3_pH[2,3] 30.363 8.020 18.413 29.772 44.946
beta3_pH[3,3] 30.010 7.840 18.458 29.263 44.736
beta3_pH[4,3] 30.226 7.982 18.466 29.540 44.960
beta3_pH[5,3] 36.668 3.862 31.208 36.088 45.040
beta3_pH[6,3] 40.442 3.431 31.858 40.756 45.620
beta3_pH[7,3] 37.964 4.228 31.368 37.834 45.363
beta3_pH[8,3] 41.491 0.254 41.055 41.491 41.934
beta3_pH[9,3] 33.451 0.583 31.572 33.527 34.231
beta3_pH[10,3] 35.850 0.780 33.564 36.026 36.860
beta3_pH[11,3] 41.810 0.812 40.135 41.843 43.274
beta3_pH[12,3] 41.728 0.397 40.962 41.737 42.492
beta3_pH[13,3] 42.714 0.900 41.030 42.704 44.720
beta3_pH[14,3] 41.107 0.575 39.915 41.135 42.162
beta3_pH[15,3] 42.649 0.651 41.252 42.711 43.753
beta3_pH[16,3] 42.904 0.737 41.116 43.015 44.056
beta4_pH[1,1] 0.901 0.695 -0.095 0.810 2.415
beta4_pH[2,1] 1.179 0.983 -0.046 0.942 3.873
beta4_pH[3,1] 0.299 0.935 -1.117 0.215 2.429
beta4_pH[4,1] 0.609 1.254 -1.319 0.505 3.582
beta4_pH[5,1] -0.615 0.619 -1.957 -0.553 0.405
beta4_pH[6,1] -0.623 0.591 -1.870 -0.591 0.363
beta4_pH[7,1] 0.343 1.311 -1.555 0.082 3.805
beta4_pH[8,1] -0.075 1.034 -1.507 -0.236 2.591
beta4_pH[9,1] 0.449 1.298 -1.313 0.114 3.812
beta4_pH[10,1] 0.646 1.241 -0.651 0.245 4.152
beta4_pH[11,1] 0.682 1.429 -1.376 0.463 4.178
beta4_pH[12,1] 0.964 1.554 -1.290 0.712 4.805
beta4_pH[13,1] 1.782 1.516 -0.257 1.479 5.639
beta4_pH[14,1] 2.016 1.626 -0.102 1.665 6.186
beta4_pH[15,1] 0.374 1.292 -1.335 0.162 3.655
beta4_pH[16,1] 0.637 1.391 -1.310 0.400 4.267
beta4_pH[1,2] -3.240 0.862 -3.967 -3.432 -0.903
beta4_pH[2,2] 0.423 2.025 -1.987 -0.157 5.630
beta4_pH[3,2] -0.861 2.158 -3.241 -1.547 4.971
beta4_pH[4,2] 1.638 1.968 -0.942 1.202 6.419
beta4_pH[5,2] 0.058 2.395 -3.537 -0.269 5.660
beta4_pH[6,2] -0.337 2.430 -3.790 -0.694 5.142
beta4_pH[7,2] 0.060 0.931 -1.703 0.025 1.941
beta4_pH[8,2] -0.763 2.149 -3.398 -1.348 4.626
beta4_pH[9,2] -0.392 2.341 -3.728 -0.711 5.008
beta4_pH[10,2] -2.436 2.093 -3.987 -3.491 3.176
beta4_pH[11,2] -0.446 0.632 -1.312 -0.544 1.032
beta4_pH[12,2] -1.072 1.035 -2.509 -1.222 1.614
beta4_pH[13,2] -1.562 0.863 -2.858 -1.664 0.367
beta4_pH[14,2] -0.131 1.049 -1.441 -0.341 2.665
beta4_pH[15,2] -1.711 0.776 -2.877 -1.825 -0.020
beta4_pH[16,2] -0.882 1.027 -2.230 -1.071 1.727
beta4_pH[1,3] -0.346 1.583 -2.252 -0.759 4.105
beta4_pH[2,3] -1.294 0.662 -2.197 -1.389 0.216
beta4_pH[3,3] -1.636 0.817 -2.714 -1.768 0.292
beta4_pH[4,3] -0.301 1.426 -1.876 -0.702 3.700
beta4_pH[5,3] 0.330 1.939 -3.411 0.208 5.035
beta4_pH[6,3] 0.461 1.816 -2.649 0.271 4.848
beta4_pH[7,3] 0.341 1.733 -2.350 0.114 4.545
beta4_pH[8,3] 0.719 1.661 -1.635 0.421 4.964
beta4_pH[9,3] 0.918 1.695 -1.524 0.625 5.183
beta4_pH[10,3] 0.165 1.667 -2.250 -0.111 4.456
beta4_pH[11,3] 0.886 1.172 -0.543 0.593 3.892
beta4_pH[12,3] 0.580 1.104 -0.994 0.385 3.342
beta4_pH[13,3] 0.033 0.625 -0.922 -0.046 1.481
beta4_pH[14,3] 0.341 0.941 -0.930 0.168 2.710
beta4_pH[15,3] 0.152 0.570 -0.731 0.081 1.536
beta4_pH[16,3] 0.628 0.976 -0.531 0.406 3.163
beta0_pelagic[1] 2.226 0.133 1.967 2.222 2.491
beta0_pelagic[2] 1.511 0.128 1.258 1.511 1.752
beta0_pelagic[3] -0.601 0.882 -2.568 -0.394 0.573
beta0_pelagic[4] -0.494 1.177 -4.483 -0.180 0.813
beta0_pelagic[5] 1.192 0.254 0.660 1.193 1.689
beta0_pelagic[6] 1.466 0.269 0.887 1.484 1.948
beta0_pelagic[7] 1.598 0.210 1.215 1.588 2.046
beta0_pelagic[8] 1.764 0.198 1.372 1.755 2.190
beta0_pelagic[9] 2.471 0.318 1.858 2.472 3.057
beta0_pelagic[10] 2.502 0.210 2.057 2.512 2.897
beta0_pelagic[11] 0.155 0.427 -0.815 0.255 0.736
beta0_pelagic[12] 1.679 0.145 1.396 1.674 1.968
beta0_pelagic[13] 0.280 0.235 -0.289 0.308 0.656
beta0_pelagic[14] -0.090 0.270 -0.704 -0.068 0.381
beta0_pelagic[15] -0.263 0.142 -0.544 -0.264 0.011
beta0_pelagic[16] 0.263 0.303 -0.558 0.332 0.664
beta1_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[3] 2.249 1.479 0.524 1.784 5.778
beta1_pelagic[4] 1.887 1.316 0.377 1.510 5.790
beta1_pelagic[5] -0.076 0.313 -0.681 -0.077 0.540
beta1_pelagic[6] -0.100 0.454 -0.870 -0.148 0.765
beta1_pelagic[7] -0.020 0.291 -0.588 -0.018 0.540
beta1_pelagic[8] -0.007 0.277 -0.561 -0.007 0.528
beta1_pelagic[9] 0.210 0.487 -0.750 0.323 0.970
beta1_pelagic[10] 0.068 0.275 -0.458 0.067 0.638
beta1_pelagic[11] 3.418 1.000 2.091 3.212 5.763
beta1_pelagic[12] 2.775 0.316 2.182 2.770 3.413
beta1_pelagic[13] 2.954 0.719 1.800 2.868 4.582
beta1_pelagic[14] 4.383 1.089 2.817 4.178 6.802
beta1_pelagic[15] 2.914 0.262 2.406 2.913 3.445
beta1_pelagic[16] 3.673 0.990 2.697 3.318 6.623
beta2_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[3] 0.486 1.343 0.030 0.150 3.691
beta2_pelagic[4] 1.283 3.117 0.033 0.373 11.387
beta2_pelagic[5] -0.010 0.675 -1.401 -0.010 1.438
beta2_pelagic[6] -0.107 0.671 -1.452 -0.154 1.298
beta2_pelagic[7] 0.013 0.643 -1.352 -0.001 1.392
beta2_pelagic[8] 0.002 0.635 -1.408 -0.002 1.329
beta2_pelagic[9] 0.206 0.684 -1.306 0.254 1.539
beta2_pelagic[10] 0.039 0.623 -1.246 0.027 1.392
beta2_pelagic[11] 2.573 5.231 0.125 0.348 16.575
beta2_pelagic[12] 6.291 5.590 0.980 4.655 21.631
beta2_pelagic[13] 1.001 2.751 0.171 0.448 5.942
beta2_pelagic[14] 0.323 0.156 0.160 0.291 0.720
beta2_pelagic[15] 6.423 5.130 1.250 4.948 20.828
beta2_pelagic[16] 4.701 5.859 0.181 2.818 20.100
beta3_pelagic[1] 29.765 7.959 18.399 28.736 44.929
beta3_pelagic[2] 29.785 7.867 18.484 28.460 44.769
beta3_pelagic[3] 28.932 6.504 18.750 28.248 43.737
beta3_pelagic[4] 24.827 4.870 18.335 24.194 39.118
beta3_pelagic[5] 29.968 8.156 18.421 28.388 45.119
beta3_pelagic[6] 31.826 6.755 18.953 31.703 44.531
beta3_pelagic[7] 29.773 7.899 18.436 28.696 44.955
beta3_pelagic[8] 29.721 8.134 18.408 28.263 44.992
beta3_pelagic[9] 30.627 6.078 19.111 30.601 42.910
beta3_pelagic[10] 29.357 8.207 18.345 27.872 45.031
beta3_pelagic[11] 42.437 1.680 38.248 42.979 45.239
beta3_pelagic[12] 43.477 0.289 43.003 43.467 43.982
beta3_pelagic[13] 42.696 1.340 39.974 42.676 45.389
beta3_pelagic[14] 42.500 1.717 39.134 42.480 45.674
beta3_pelagic[15] 43.167 0.282 42.473 43.176 43.690
beta3_pelagic[16] 43.111 0.814 41.094 43.196 45.018
mu_beta0_pelagic[1] 0.636 1.158 -2.041 0.710 2.862
mu_beta0_pelagic[2] 1.803 0.396 1.008 1.804 2.579
mu_beta0_pelagic[3] 0.341 0.453 -0.602 0.352 1.271
tau_beta0_pelagic[1] 0.445 0.500 0.048 0.278 1.866
tau_beta0_pelagic[2] 2.841 3.236 0.248 2.058 9.726
tau_beta0_pelagic[3] 1.578 1.211 0.167 1.266 4.714
beta0_yellow[1] -0.532 0.194 -0.987 -0.515 -0.213
beta0_yellow[2] 0.505 0.163 0.159 0.511 0.799
beta0_yellow[3] -0.315 0.191 -0.713 -0.309 0.022
beta0_yellow[4] 0.832 0.315 -0.053 0.894 1.212
beta0_yellow[5] -0.282 0.354 -0.952 -0.279 0.414
beta0_yellow[6] 1.111 0.168 0.789 1.112 1.441
beta0_yellow[7] 0.983 0.155 0.687 0.976 1.295
beta0_yellow[8] 1.011 0.153 0.716 1.009 1.310
beta0_yellow[9] 0.661 0.161 0.345 0.656 0.973
beta0_yellow[10] 0.592 0.142 0.308 0.594 0.874
beta0_yellow[11] -1.979 0.486 -2.929 -1.987 -1.032
beta0_yellow[12] -3.710 0.420 -4.603 -3.695 -2.946
beta0_yellow[13] -3.738 0.486 -4.783 -3.717 -2.856
beta0_yellow[14] -2.162 0.550 -3.162 -2.185 -0.883
beta0_yellow[15] -2.877 0.447 -3.805 -2.856 -2.047
beta0_yellow[16] -2.398 0.467 -3.318 -2.404 -1.432
beta1_yellow[1] 0.857 1.483 0.010 0.667 2.717
beta1_yellow[2] 1.065 0.358 0.582 1.026 1.701
beta1_yellow[3] 0.705 0.264 0.247 0.692 1.250
beta1_yellow[4] 1.377 0.813 0.617 1.170 4.013
beta1_yellow[5] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[6] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[7] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[8] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[9] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[10] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[11] 2.121 0.479 1.182 2.117 3.066
beta1_yellow[12] 2.507 0.437 1.690 2.486 3.423
beta1_yellow[13] 2.861 0.491 2.005 2.835 3.908
beta1_yellow[14] 2.234 0.532 1.098 2.254 3.248
beta1_yellow[15] 2.125 0.440 1.302 2.100 3.044
beta1_yellow[16] 2.156 0.476 1.221 2.163 3.083
beta2_yellow[1] -4.084 3.318 -12.102 -3.334 -0.091
beta2_yellow[2] -4.190 3.489 -12.545 -3.180 -0.230
beta2_yellow[3] -3.935 3.466 -13.554 -3.010 -0.160
beta2_yellow[4] -3.353 3.277 -11.326 -2.312 -0.085
beta2_yellow[5] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[6] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[7] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[8] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[9] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[10] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[11] -4.501 2.651 -11.461 -3.919 -1.099
beta2_yellow[12] -4.852 2.537 -11.377 -4.321 -1.444
beta2_yellow[13] -4.625 2.484 -10.760 -4.041 -1.497
beta2_yellow[14] -4.650 2.738 -11.539 -4.123 -0.674
beta2_yellow[15] -4.346 2.668 -11.211 -3.713 -1.040
beta2_yellow[16] -4.875 2.646 -11.347 -4.314 -1.372
beta3_yellow[1] 25.820 7.207 18.245 22.608 44.127
beta3_yellow[2] 29.100 1.759 26.290 28.860 32.811
beta3_yellow[3] 32.955 3.058 26.339 32.844 39.556
beta3_yellow[4] 29.009 3.487 21.503 28.000 35.921
beta3_yellow[5] 29.993 7.918 18.448 29.055 44.822
beta3_yellow[6] 30.139 8.033 18.492 29.256 44.982
beta3_yellow[7] 30.089 7.921 18.526 29.169 45.049
beta3_yellow[8] 29.977 7.870 18.528 29.086 44.705
beta3_yellow[9] 30.180 8.047 18.442 29.387 44.876
beta3_yellow[10] 30.007 7.911 18.477 29.099 44.978
beta3_yellow[11] 45.285 0.722 43.947 45.415 45.973
beta3_yellow[12] 43.302 0.373 42.554 43.276 44.071
beta3_yellow[13] 44.858 0.407 43.973 44.929 45.526
beta3_yellow[14] 44.159 1.481 42.849 44.269 45.845
beta3_yellow[15] 45.169 0.524 44.162 45.155 45.965
beta3_yellow[16] 44.533 0.826 43.353 44.546 45.843
mu_beta0_yellow[1] 0.106 0.558 -1.082 0.116 1.260
mu_beta0_yellow[2] 0.652 0.325 -0.032 0.668 1.287
mu_beta0_yellow[3] -2.458 0.654 -3.507 -2.549 -0.866
tau_beta0_yellow[1] 1.790 2.408 0.093 1.127 7.538
tau_beta0_yellow[2] 3.724 4.652 0.336 2.503 14.749
tau_beta0_yellow[3] 1.501 2.634 0.090 0.908 6.062
beta0_black[1] -0.074 0.160 -0.379 -0.078 0.241
beta0_black[2] 1.917 0.130 1.665 1.918 2.173
beta0_black[3] 1.317 0.136 1.058 1.317 1.586
beta0_black[4] 2.430 0.130 2.177 2.432 2.679
beta0_black[5] 4.630 2.102 1.877 4.196 10.043
beta0_black[6] 4.586 1.924 2.266 4.088 9.853
beta0_black[7] 3.728 1.896 1.515 3.240 8.802
beta0_black[8] 0.958 0.212 0.554 0.953 1.375
beta0_black[9] 2.607 0.226 2.166 2.606 3.043
beta0_black[10] 1.464 0.135 1.201 1.467 1.733
beta0_black[11] 3.485 0.155 3.180 3.488 3.779
beta0_black[12] 4.867 0.175 4.533 4.864 5.203
beta0_black[13] -0.109 0.251 -0.607 -0.097 0.338
beta0_black[14] 2.852 0.162 2.538 2.856 3.158
beta0_black[15] 1.289 0.154 0.994 1.286 1.600
beta0_black[16] 4.275 0.162 3.952 4.274 4.590
beta2_black[1] 7.771 10.008 0.542 3.449 40.294
beta2_black[2] 0.000 0.000 0.000 0.000 0.000
beta2_black[3] 0.000 0.000 0.000 0.000 0.000
beta2_black[4] 0.000 0.000 0.000 0.000 0.000
beta2_black[5] 0.000 0.000 0.000 0.000 0.000
beta2_black[6] 0.000 0.000 0.000 0.000 0.000
beta2_black[7] 0.000 0.000 0.000 0.000 0.000
beta2_black[8] 0.000 0.000 0.000 0.000 0.000
beta2_black[9] 0.000 0.000 0.000 0.000 0.000
beta2_black[10] 0.000 0.000 0.000 0.000 0.000
beta2_black[11] 0.000 0.000 0.000 0.000 0.000
beta2_black[12] 0.000 0.000 0.000 0.000 0.000
beta2_black[13] -2.237 1.813 -7.313 -1.662 -0.406
beta2_black[14] 0.000 0.000 0.000 0.000 0.000
beta2_black[15] 0.000 0.000 0.000 0.000 0.000
beta2_black[16] 0.000 0.000 0.000 0.000 0.000
beta3_black[1] 41.743 1.342 39.695 41.952 43.251
beta3_black[2] 25.000 0.000 25.000 25.000 25.000
beta3_black[3] 25.000 0.000 25.000 25.000 25.000
beta3_black[4] 25.000 0.000 25.000 25.000 25.000
beta3_black[5] 25.000 0.000 25.000 25.000 25.000
beta3_black[6] 25.000 0.000 25.000 25.000 25.000
beta3_black[7] 25.000 0.000 25.000 25.000 25.000
beta3_black[8] 25.000 0.000 25.000 25.000 25.000
beta3_black[9] 25.000 0.000 25.000 25.000 25.000
beta3_black[10] 25.000 0.000 25.000 25.000 25.000
beta3_black[11] 25.000 0.000 25.000 25.000 25.000
beta3_black[12] 25.000 0.000 25.000 25.000 25.000
beta3_black[13] 39.278 0.775 37.516 39.340 40.591
beta3_black[14] 25.000 0.000 25.000 25.000 25.000
beta3_black[15] 25.000 0.000 25.000 25.000 25.000
beta3_black[16] 25.000 0.000 25.000 25.000 25.000
beta4_black[1] -0.263 0.197 -0.659 -0.264 0.126
beta4_black[2] 0.242 0.190 -0.129 0.236 0.615
beta4_black[3] -0.935 0.198 -1.322 -0.933 -0.548
beta4_black[4] 0.424 0.215 0.007 0.426 0.841
beta4_black[5] 0.521 1.239 -1.214 0.331 3.480
beta4_black[6] 0.557 1.239 -1.199 0.331 3.830
beta4_black[7] 0.399 1.136 -1.374 0.241 3.183
beta4_black[8] -0.248 0.314 -0.898 -0.231 0.361
beta4_black[9] 0.837 0.767 -0.258 0.704 2.715
beta4_black[10] 0.050 0.184 -0.317 0.052 0.414
beta4_black[11] -0.698 0.215 -1.094 -0.696 -0.284
beta4_black[12] 0.164 0.322 -0.435 0.155 0.829
beta4_black[13] -1.185 0.223 -1.617 -1.185 -0.744
beta4_black[14] -0.183 0.238 -0.626 -0.190 0.293
beta4_black[15] -0.882 0.214 -1.316 -0.881 -0.462
beta4_black[16] -0.596 0.230 -1.052 -0.599 -0.150
mu_beta0_black[1] 1.286 0.911 -0.728 1.326 3.109
mu_beta0_black[2] 2.714 1.048 0.805 2.611 5.141
mu_beta0_black[3] 2.528 0.970 0.451 2.579 4.438
tau_beta0_black[1] 0.613 0.577 0.057 0.435 2.178
tau_beta0_black[2] 0.453 0.588 0.046 0.252 2.063
tau_beta0_black[3] 0.240 0.161 0.050 0.203 0.634
beta0_dsr[11] -2.882 0.291 -3.431 -2.879 -2.300
beta0_dsr[12] 4.543 0.302 3.997 4.541 5.113
beta0_dsr[13] -1.348 0.299 -1.960 -1.341 -0.775
beta0_dsr[14] -3.656 0.502 -4.618 -3.662 -2.666
beta0_dsr[15] -1.935 0.284 -2.508 -1.929 -1.406
beta0_dsr[16] -2.988 0.368 -3.716 -2.992 -2.260
beta1_dsr[11] 4.819 0.302 4.223 4.826 5.431
beta1_dsr[12] 7.463 22.307 2.294 5.031 20.475
beta1_dsr[13] 2.862 0.313 2.275 2.850 3.483
beta1_dsr[14] 6.323 0.530 5.292 6.317 7.319
beta1_dsr[15] 3.333 0.292 2.760 3.332 3.918
beta1_dsr[16] 5.806 0.385 5.073 5.798 6.573
beta2_dsr[11] -8.150 2.383 -13.654 -7.942 -4.296
beta2_dsr[12] -7.096 2.633 -12.761 -6.939 -2.372
beta2_dsr[13] -6.455 2.634 -12.088 -6.328 -1.937
beta2_dsr[14] -6.207 2.650 -11.960 -6.001 -1.902
beta2_dsr[15] -7.770 2.526 -13.355 -7.464 -3.784
beta2_dsr[16] -7.880 2.371 -13.413 -7.541 -4.160
beta3_dsr[11] 43.488 0.149 43.211 43.486 43.769
beta3_dsr[12] 33.982 0.836 32.088 34.142 34.815
beta3_dsr[13] 43.248 0.288 42.824 43.193 43.861
beta3_dsr[14] 43.352 0.240 43.077 43.282 43.952
beta3_dsr[15] 43.504 0.189 43.154 43.508 43.851
beta3_dsr[16] 43.437 0.159 43.166 43.423 43.756
beta4_dsr[11] 0.582 0.218 0.163 0.579 1.016
beta4_dsr[12] 0.238 0.442 -0.639 0.236 1.084
beta4_dsr[13] -0.166 0.223 -0.608 -0.158 0.255
beta4_dsr[14] 0.147 0.255 -0.368 0.149 0.638
beta4_dsr[15] 0.722 0.215 0.306 0.723 1.149
beta4_dsr[16] 0.155 0.230 -0.300 0.154 0.609
beta0_slope[11] -1.844 0.146 -2.142 -1.846 -1.556
beta0_slope[12] -4.473 0.266 -5.014 -4.466 -3.981
beta0_slope[13] -1.338 0.185 -1.738 -1.325 -1.020
beta0_slope[14] -2.674 0.166 -2.999 -2.679 -2.344
beta0_slope[15] -1.336 0.149 -1.637 -1.334 -1.047
beta0_slope[16] -2.741 0.159 -3.051 -2.745 -2.423
beta1_slope[11] 4.486 0.224 4.047 4.488 4.931
beta1_slope[12] 3.992 0.450 3.148 3.990 4.840
beta1_slope[13] 2.727 0.461 2.197 2.646 4.133
beta1_slope[14] 6.322 0.416 5.528 6.309 7.166
beta1_slope[15] 2.999 0.204 2.601 3.001 3.397
beta1_slope[16] 5.288 0.286 4.712 5.285 5.841
beta2_slope[11] 8.685 2.332 5.106 8.347 14.237
beta2_slope[12] 6.612 2.937 1.181 6.659 12.562
beta2_slope[13] 5.336 3.084 0.388 5.222 11.644
beta2_slope[14] 6.374 2.514 2.244 6.210 11.954
beta2_slope[15] 8.177 2.385 4.406 7.846 13.722
beta2_slope[16] 7.817 2.308 4.173 7.518 13.346
beta3_slope[11] 43.461 0.134 43.218 43.458 43.724
beta3_slope[12] 43.348 0.302 42.845 43.317 43.942
beta3_slope[13] 43.459 0.402 42.918 43.398 44.083
beta3_slope[14] 43.266 0.136 43.090 43.233 43.616
beta3_slope[15] 43.485 0.160 43.196 43.482 43.790
beta3_slope[16] 43.372 0.145 43.150 43.352 43.716
beta4_slope[11] -0.727 0.163 -1.049 -0.725 -0.404
beta4_slope[12] -1.152 0.462 -2.146 -1.118 -0.344
beta4_slope[13] 0.082 0.164 -0.235 0.080 0.399
beta4_slope[14] -0.091 0.195 -0.482 -0.089 0.288
beta4_slope[15] -0.767 0.160 -1.083 -0.767 -0.458
beta4_slope[16] -0.158 0.175 -0.499 -0.157 0.183
sigma_H[1] 0.200 0.055 0.101 0.196 0.314
sigma_H[2] 0.171 0.031 0.117 0.169 0.238
sigma_H[3] 0.197 0.043 0.118 0.195 0.289
sigma_H[4] 0.419 0.078 0.293 0.411 0.597
sigma_H[5] 0.990 0.209 0.615 0.985 1.428
sigma_H[6] 0.438 0.195 0.066 0.427 0.834
sigma_H[7] 0.311 0.065 0.211 0.303 0.463
sigma_H[8] 0.415 0.089 0.275 0.407 0.605
sigma_H[9] 0.524 0.129 0.331 0.503 0.816
sigma_H[10] 0.212 0.043 0.137 0.209 0.310
sigma_H[11] 0.277 0.046 0.202 0.273 0.380
sigma_H[12] 0.438 0.164 0.210 0.412 0.776
sigma_H[13] 0.214 0.038 0.147 0.210 0.298
sigma_H[14] 0.507 0.091 0.351 0.501 0.703
sigma_H[15] 0.247 0.041 0.176 0.244 0.337
sigma_H[16] 0.224 0.044 0.153 0.219 0.324
lambda_H[1] 3.232 4.295 0.137 1.844 14.281
lambda_H[2] 8.131 7.449 0.800 5.975 26.740
lambda_H[3] 6.397 9.647 0.269 3.226 33.045
lambda_H[4] 0.006 0.004 0.001 0.005 0.018
lambda_H[5] 4.046 9.225 0.038 1.086 28.900
lambda_H[6] 6.550 13.268 0.008 0.892 43.902
lambda_H[7] 0.013 0.009 0.002 0.011 0.035
lambda_H[8] 8.012 9.913 0.135 4.640 35.529
lambda_H[9] 0.015 0.010 0.003 0.013 0.039
lambda_H[10] 0.336 1.246 0.032 0.198 1.151
lambda_H[11] 0.262 0.409 0.011 0.128 1.222
lambda_H[12] 4.809 6.488 0.183 2.728 23.534
lambda_H[13] 3.394 3.059 0.233 2.597 10.941
lambda_H[14] 3.421 4.364 0.247 1.990 14.861
lambda_H[15] 0.029 0.182 0.004 0.017 0.103
lambda_H[16] 0.825 1.157 0.042 0.428 3.901
mu_lambda_H[1] 4.410 1.911 1.266 4.265 8.511
mu_lambda_H[2] 3.873 1.983 0.670 3.648 7.972
mu_lambda_H[3] 3.454 1.821 0.761 3.167 7.455
sigma_lambda_H[1] 8.827 4.310 2.140 8.203 18.407
sigma_lambda_H[2] 8.405 4.714 1.116 7.882 18.473
sigma_lambda_H[3] 6.212 3.984 0.960 5.373 16.279
beta_H[1,1] 6.890 1.116 4.090 7.100 8.510
beta_H[2,1] 9.879 0.483 8.828 9.904 10.761
beta_H[3,1] 8.017 0.778 6.160 8.106 9.312
beta_H[4,1] 9.468 7.663 -6.793 9.705 23.847
beta_H[5,1] 0.141 2.237 -4.624 0.300 3.944
beta_H[6,1] 3.083 4.010 -7.245 4.480 7.835
beta_H[7,1] 0.637 5.611 -11.592 1.084 10.713
beta_H[8,1] 1.322 3.755 -2.468 1.229 3.481
beta_H[9,1] 12.965 5.702 1.004 13.112 23.956
beta_H[10,1] 7.009 1.685 3.603 7.064 10.285
beta_H[11,1] 5.045 3.512 -2.879 5.791 9.844
beta_H[12,1] 2.638 1.050 0.845 2.549 4.877
beta_H[13,1] 9.029 0.908 7.081 9.095 10.504
beta_H[14,1] 2.184 1.001 0.246 2.203 4.114
beta_H[15,1] -5.940 3.793 -12.800 -6.130 2.237
beta_H[16,1] 3.395 2.601 -0.775 3.061 9.333
beta_H[1,2] 7.908 0.247 7.406 7.911 8.373
beta_H[2,2] 10.027 0.137 9.756 10.029 10.294
beta_H[3,2] 8.953 0.197 8.562 8.954 9.343
beta_H[4,2] 3.545 1.450 0.865 3.512 6.438
beta_H[5,2] 1.955 0.924 0.170 1.961 3.745
beta_H[6,2] 5.714 1.030 3.269 5.887 7.314
beta_H[7,2] 2.630 1.059 0.788 2.562 4.837
beta_H[8,2] 3.002 1.043 1.477 3.127 4.253
beta_H[9,2] 3.537 1.108 1.534 3.501 5.854
beta_H[10,2] 8.204 0.340 7.492 8.210 8.868
beta_H[11,2] 9.764 0.637 8.828 9.641 11.214
beta_H[12,2] 3.954 0.369 3.288 3.934 4.731
beta_H[13,2] 9.122 0.250 8.679 9.111 9.623
beta_H[14,2] 4.013 0.355 3.348 4.018 4.718
beta_H[15,2] 11.331 0.682 9.907 11.364 12.571
beta_H[16,2] 4.528 0.809 2.985 4.515 6.202
beta_H[1,3] 8.454 0.247 8.015 8.435 8.975
beta_H[2,3] 10.065 0.115 9.842 10.063 10.293
beta_H[3,3] 9.614 0.166 9.295 9.612 9.965
beta_H[4,3] -2.477 0.870 -4.229 -2.460 -0.773
beta_H[5,3] 3.832 0.596 2.614 3.822 4.993
beta_H[6,3] 7.964 1.194 6.366 7.611 10.617
beta_H[7,3] -2.776 0.640 -4.063 -2.750 -1.556
beta_H[8,3] 5.232 0.480 4.638 5.169 6.099
beta_H[9,3] -2.876 0.733 -4.345 -2.871 -1.516
beta_H[10,3] 8.674 0.282 8.114 8.675 9.230
beta_H[11,3] 8.541 0.284 7.928 8.565 9.032
beta_H[12,3] 5.250 0.320 4.510 5.286 5.777
beta_H[13,3] 8.846 0.176 8.480 8.849 9.190
beta_H[14,3] 5.723 0.277 5.118 5.747 6.212
beta_H[15,3] 10.380 0.319 9.755 10.382 11.009
beta_H[16,3] 6.264 0.609 4.967 6.324 7.283
beta_H[1,4] 8.259 0.183 7.869 8.274 8.587
beta_H[2,4] 10.128 0.119 9.880 10.136 10.336
beta_H[3,4] 10.120 0.161 9.756 10.134 10.398
beta_H[4,4] 11.789 0.456 10.855 11.801 12.649
beta_H[5,4] 5.488 0.733 4.297 5.398 7.158
beta_H[6,4] 6.986 0.953 4.895 7.273 8.282
beta_H[7,4] 8.275 0.338 7.593 8.278 8.939
beta_H[8,4] 6.713 0.242 6.275 6.727 7.120
beta_H[9,4] 7.219 0.475 6.298 7.220 8.153
beta_H[10,4] 7.732 0.239 7.299 7.726 8.234
beta_H[11,4] 9.385 0.203 8.996 9.385 9.777
beta_H[12,4] 7.139 0.211 6.734 7.134 7.589
beta_H[13,4] 9.044 0.141 8.749 9.045 9.318
beta_H[14,4] 7.733 0.216 7.309 7.731 8.185
beta_H[15,4] 9.461 0.239 8.976 9.466 9.921
beta_H[16,4] 9.350 0.235 8.925 9.342 9.864
beta_H[1,5] 8.982 0.146 8.681 8.986 9.260
beta_H[2,5] 10.785 0.095 10.607 10.782 10.976
beta_H[3,5] 10.918 0.171 10.616 10.910 11.269
beta_H[4,5] 8.397 0.467 7.503 8.390 9.333
beta_H[5,5] 5.438 0.583 3.977 5.479 6.435
beta_H[6,5] 8.869 0.646 7.968 8.708 10.424
beta_H[7,5] 6.753 0.335 6.130 6.750 7.453
beta_H[8,5] 8.215 0.206 7.860 8.203 8.620
beta_H[9,5] 8.195 0.485 7.236 8.203 9.162
beta_H[10,5] 10.090 0.234 9.620 10.088 10.545
beta_H[11,5] 11.513 0.235 11.050 11.515 11.988
beta_H[12,5] 8.484 0.193 8.117 8.481 8.881
beta_H[13,5] 10.012 0.128 9.755 10.014 10.261
beta_H[14,5] 9.196 0.236 8.758 9.184 9.691
beta_H[15,5] 11.168 0.246 10.699 11.163 11.657
beta_H[16,5] 9.925 0.182 9.549 9.928 10.277
beta_H[1,6] 10.179 0.192 9.846 10.165 10.603
beta_H[2,6] 11.511 0.105 11.308 11.511 11.715
beta_H[3,6] 10.816 0.162 10.461 10.827 11.109
beta_H[4,6] 12.867 0.827 11.161 12.898 14.473
beta_H[5,6] 5.881 0.609 4.713 5.875 7.117
beta_H[6,6] 8.816 0.721 6.839 8.963 9.804
beta_H[7,6] 9.865 0.575 8.724 9.864 10.991
beta_H[8,6] 9.525 0.266 9.013 9.542 9.956
beta_H[9,6] 8.475 0.819 6.882 8.460 10.080
beta_H[10,6] 9.507 0.312 8.829 9.534 10.046
beta_H[11,6] 10.818 0.349 10.091 10.838 11.454
beta_H[12,6] 9.374 0.256 8.871 9.370 9.894
beta_H[13,6] 11.052 0.165 10.764 11.038 11.397
beta_H[14,6] 9.827 0.294 9.220 9.833 10.361
beta_H[15,6] 10.834 0.431 9.942 10.846 11.653
beta_H[16,6] 10.542 0.241 10.028 10.551 10.995
beta_H[1,7] 10.878 0.877 8.822 10.987 12.311
beta_H[2,7] 12.213 0.428 11.314 12.219 13.066
beta_H[3,7] 10.553 0.666 9.042 10.623 11.669
beta_H[4,7] 2.585 4.203 -5.452 2.454 11.081
beta_H[5,7] 6.295 1.762 2.973 6.292 9.871
beta_H[6,7] 9.810 2.567 4.767 9.701 16.601
beta_H[7,7] 10.544 2.930 4.776 10.580 16.398
beta_H[8,7] 10.957 0.962 9.498 10.912 12.512
beta_H[9,7] 4.380 4.135 -3.841 4.511 12.394
beta_H[10,7] 9.831 1.447 7.221 9.716 12.966
beta_H[11,7] 10.915 1.760 7.582 10.805 14.839
beta_H[12,7] 10.003 0.971 7.861 10.095 11.611
beta_H[13,7] 11.646 0.754 9.879 11.739 12.793
beta_H[14,7] 10.408 0.953 8.375 10.466 12.030
beta_H[15,7] 12.026 2.224 7.753 11.987 16.503
beta_H[16,7] 12.304 1.300 10.155 12.157 15.361
beta0_H[1] 8.767 14.063 -19.954 9.031 36.046
beta0_H[2] 10.617 6.539 -2.935 10.543 23.466
beta0_H[3] 10.197 10.509 -9.611 9.925 30.900
beta0_H[4] 6.598 184.851 -361.471 7.323 378.123
beta0_H[5] 4.536 21.712 -41.094 4.473 50.306
beta0_H[6] 7.074 52.122 -113.013 7.575 122.749
beta0_H[7] 4.796 135.348 -260.032 3.956 278.664
beta0_H[8] 7.114 35.051 -14.839 6.516 27.388
beta0_H[9] 1.056 125.533 -246.480 0.921 252.156
beta0_H[10] 7.925 33.820 -63.354 8.623 75.784
beta0_H[11] 8.659 51.512 -103.844 9.445 115.414
beta0_H[12] 6.838 12.006 -16.466 6.672 30.585
beta0_H[13] 9.907 11.386 -11.032 9.757 32.067
beta0_H[14] 6.872 11.563 -15.851 7.104 29.217
beta0_H[15] 7.282 103.083 -201.590 6.032 217.250
beta0_H[16] 7.956 25.612 -40.269 7.659 60.801